Question

Через первую трубу можно наполнить бак водой за 4 мин. через вторую за 12 минут . За сколько минут можно на полнить бак через две трубы?

Answer 1

Весь бак принимаем за целое (1) :

1) 1 : 4 = 1/4 бака - наполняет I труба за 1 мин.
2) 1 : 12 = 1/12 бака - наполняет II труба за 1 мин.
3) 1/4 + 1/12 = 3/12 + 1/12 = 4/12 = 1/3 бака - совместная производительность за 1 мин.
4) 1 : 1/3 = 1 * 3 = 3 мин. - за столько можно наполнить бак через две трубы - ответ.

Answer 2

Problem Analysis

We are given two pipes, one of which can fill a tank with water in 4 minutes, and the other can fill the same tank in 12 minutes. We need to determine how long it will take to fill the tank if both pipes are used simultaneously.

Solution

To solve this problem, we can calculate the rate at which each pipe fills the tank and then add the rates together to find the combined rate. Finally, we can use the combined rate to calculate the time it takes to fill the tank.

Let's denote the rate at which the first pipe fills the tank as R1 and the rate at which the second pipe fills the tank as R2. The time it takes to fill the tank using both pipes can be calculated using the formula:

Time = Volume / (R1 + R2)

Since the volume of the tank is not given, we can assume it to be 1 unit for simplicity. Therefore, the time it takes to fill the tank using both pipes is:

Time = 1 / (R1 + R2)

To find the rates at which each pipe fills the tank, we can use the formula:

Rate = Volume / Time

For the first pipe, the rate is:

R1 = 1 / 4 = 0.25 units per minute

For the second pipe, the rate is:

R2 = 1 / 12 = 0.0833 units per minute

Now, we can substitute the values of R1 and R2 into the formula to find the time it takes to fill the tank using both pipes:

Time = 1 / (0.25 + 0.0833) = 1 / 0.3333 ≈ 3 minutes

Therefore, it will take approximately 3 minutes to fill the tank using both pipes.

Answer

It will take approximately 3 minutes to fill the tank using both pipes.

Verification

To verify the answer, we can calculate the volume of water filled by each pipe in 3 minutes and check if the sum of the volumes is equal to the volume of the tank.

The volume filled by the first pipe in 3 minutes is:

Volume1 = Rate1 * Time = 0.25 * 3 = 0.75 units

The volume filled by the second pipe in 3 minutes is:

Volume2 = Rate2 * Time = 0.0833 * 3 = 0.25 units

The sum of the volumes filled by both pipes is:

Volume1 + Volume2 = 0.75 + 0.25 = 1 unit

Since the sum of the volumes is equal to the volume of the tank, the answer is verified.

Conclusion

It will take approximately 3 minutes to fill the tank using both pipes.